code chunk
pacman::p_load(sf, raster, spatstat, tmap, tidyverse)Hands-on Exercise 2a: 1st Order Spatial Point Patterns Analysis Methods
In this exercise, we will learn to analyze spatial point patterns in R, including importing geospatial data, performing kernel density estimation and nearest neighbor analysis, and visualizing results using spatstat, sf, and tmap packages.
1 Overview
Spatial Point Pattern Analysis is the evaluation of the pattern or distribution, of a set of points on a surface. The point can be location of:
- Events such as crime, traffic accident and disease onset, or
- Business services (coffee and fastfood outlets) or facilities such as childcare and eldercare.
We’ll use appropriate functions from spatstat to discover spatial point processes of childcare centres in Singapore.
2 The data
Data sets in this exercise are as follows:
CHILDCARE(Point Feature Data)- This dataset provides both location and attribute information of childcare centres across Singapore.
- Format: GeoJSON
- Source: data.gov.sg
MP14_SUBZONE_WEB_PL(Polygon Feature Data)- This dataset provide information of URA 2014 Master Plan Planning Subzone boundary data.
- Format: ESRI Shapefile.
- Source: data.gov.sg
CostalOutline(Polygon Feature Data)- This dataset shows the national boundary of Singapore.
- Format: ESRI Shapefile
- Source: Singapore Land Authority
3 Installing and loading R packages
The code chunk below install and load following packages into R environment:
- sf, a relatively new R package specially designed to import, manage and process vector-based geospatial data in R.
- spatstat, which has a wide range of useful functions for point pattern analysis. In this hands-on exercise, it will be used to perform 1st- and 2nd-order spatial point patterns analysis and derive kernel density estimation (KDE) layer.
- raster which reads, writes, manipulates, analyses and model of gridded spatial data (i.e. raster). In this hands-on exercise, it will be used to convert image output generate by spatstat into raster format.
- maptools which provides a set of tools for manipulating geographic data. In this hands-on exercise, we mainly use it to convert Spatial objects into ppp format of spatstat.
- tmap which provides functions for plotting cartographic quality static point patterns maps or interactive maps by using leaflet API.
4 Spatial data wrangling
4.1 Importing spatial data
We will use st_read() of sf package will be used to import these three geospatial data sets into R.
Since the childcare_sf simple feature data frame is in the WGS84 geodetic CRS, which is not ideal for geospatial analysis, the st_transform() function from the sf package is used to reproject the data to the SVY21 coordinate system during import.
code chunk
childcare_sf <- st_read("data/child-care-services-geojson.geojson") %>%
st_transform(crs = 3414)Reading layer `child-care-services-geojson' from data source
`/Users/cham/project/Geospatial-Analytics/chrismanafe/ISSS626-GAA/hands_on_ex/hands_on_ex02/data/child-care-services-geojson.geojson'
using driver `GeoJSON'
Simple feature collection with 1545 features and 2 fields
Geometry type: POINT
Dimension: XYZ
Bounding box: xmin: 103.6824 ymin: 1.248403 xmax: 103.9897 ymax: 1.462134
z_range: zmin: 0 zmax: 0
Geodetic CRS: WGS 84Let’s verify the crs of the data frame to ensure we’re using EPSG 3414.
code chunk
st_crs(childcare_sf)Coordinate Reference System:
User input: EPSG:3414
wkt:
PROJCRS["SVY21 / Singapore TM",
BASEGEOGCRS["SVY21",
DATUM["SVY21",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4757]],
CONVERSION["Singapore Transverse Mercator",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["northing (N)",north,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["easting (E)",east,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Cadastre, engineering survey, topographic mapping."],
AREA["Singapore - onshore and offshore."],
BBOX[1.13,103.59,1.47,104.07]],
ID["EPSG",3414]]Import coastal outline data using st_read() function
code chunk
sg_sf <- st_read(dsn = "data", layer="CostalOutline")Reading layer `CostalOutline' from data source
`/Users/cham/project/Geospatial-Analytics/chrismanafe/ISSS626-GAA/hands_on_ex/hands_on_ex02/data'
using driver `ESRI Shapefile'
Simple feature collection with 60 features and 4 fields
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 2663.926 ymin: 16357.98 xmax: 56047.79 ymax: 50244.03
Projected CRS: SVY21Let’s check coordinate system of this data frame
code chunk
st_crs(sg_sf)Coordinate Reference System:
User input: SVY21
wkt:
PROJCRS["SVY21",
BASEGEOGCRS["SVY21[WGS84]",
DATUM["World Geodetic System 1984",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]],
ID["EPSG",6326]],
PRIMEM["Greenwich",0,
ANGLEUNIT["Degree",0.0174532925199433]]],
CONVERSION["unnamed",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["(E)",east,
ORDER[1],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]],
AXIS["(N)",north,
ORDER[2],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]]]Coastal outline data frame is using EPSG 9001 instead of 3414 which is suitable for CRS SVY21. Let’s assign correct EPSG code using st_set_crs() then verify the output.
code chunk
sg_sf = st_set_crs(sg_sf, 3414)Warning: st_crs<- : replacing crs does not reproject data; use st_transform for
thatcode chunk
st_crs(sg_sf)Coordinate Reference System:
User input: EPSG:3414
wkt:
PROJCRS["SVY21 / Singapore TM",
BASEGEOGCRS["SVY21",
DATUM["SVY21",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4757]],
CONVERSION["Singapore Transverse Mercator",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["northing (N)",north,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["easting (E)",east,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Cadastre, engineering survey, topographic mapping."],
AREA["Singapore - onshore and offshore."],
BBOX[1.13,103.59,1.47,104.07]],
ID["EPSG",3414]]Let’s load the Master Plan Planning data using st_read() function
code chunk
mpsz_sf <- st_read(dsn = "data",
layer = "MP14_SUBZONE_WEB_PL")Reading layer `MP14_SUBZONE_WEB_PL' from data source
`/Users/cham/project/Geospatial-Analytics/chrismanafe/ISSS626-GAA/hands_on_ex/hands_on_ex02/data'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21Let’s check coordinate system of this data frame
code chunk
st_crs(mpsz_sf)Coordinate Reference System:
User input: SVY21
wkt:
PROJCRS["SVY21",
BASEGEOGCRS["SVY21[WGS84]",
DATUM["World Geodetic System 1984",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]],
ID["EPSG",6326]],
PRIMEM["Greenwich",0,
ANGLEUNIT["Degree",0.0174532925199433]]],
CONVERSION["unnamed",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["(E)",east,
ORDER[1],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]],
AXIS["(N)",north,
ORDER[2],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]]]mpsz_sf is also using EPSG 9001 instead of 3414 which is suitable for CRS SVY21. Let’s assign correct EPSG code using st_set_crs() then verify the output.
code chunk
mpsz_sf <- st_set_crs(mpsz_sf,3414)Warning: st_crs<- : replacing crs does not reproject data; use st_transform for
thatcode chunk
st_crs(mpsz_sf)Coordinate Reference System:
User input: EPSG:3414
wkt:
PROJCRS["SVY21 / Singapore TM",
BASEGEOGCRS["SVY21",
DATUM["SVY21",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4757]],
CONVERSION["Singapore Transverse Mercator",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["northing (N)",north,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["easting (E)",east,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Cadastre, engineering survey, topographic mapping."],
AREA["Singapore - onshore and offshore."],
BBOX[1.13,103.59,1.47,104.07]],
ID["EPSG",3414]]4.2 Mapping the geospatial data sets
After checking the referencing system of each geospatial data data frame, it is also useful for us to plot a map to show their spatial patterns.
code chunk
tm_shape(mpsz_sf) +
tm_polygons() +
tm_shape(childcare_sf) +
tm_dots()
Notice that all the geospatial layers are within the same map extend. This shows that their referencing system and coordinate values are referred to similar spatial context. This is very important in any geospatial analysis.
Alternatively, we can also prepare a pin map by using the code chunk below.
code chunk
tmap_mode('view')tmap mode set to interactive viewingcode chunk
tm_shape(childcare_sf)+
tm_dots()code chunk
tmap_mode('plot')tmap mode set to plottingIn interactive mode, tmap uses the Leaflet for R API. This interactive pin map offers several advantages, including the ability to freely navigate and zoom around the map. We can also query information of each simple feature (i.e. the point) by clicking of them. Additionally, you can change the background of the map layer. Currently, three internet map layers are available: ESRI.WorldGrayCanvas (the default), OpenStreetMap, and ESRI.WorldTopoMap.
Note
Reminder: After using an interactive map, be sure to switch back to plot mode. Each interactive session consumes a connection, and displaying too many interactive maps (ideally no more than 10) in a single RMarkdown document can cause issues when publishing on Netlify.
5 Geospatial data wrangling
5.1 Converting sf data frame into sp’s Spatial* class
Although simple feature data frame is gaining popularity again sp’s Spatial* classes, there are, however, many geospatial analysis packages require the input geospatial data in sp’s Spatial* classes. In this section, we will learn how to convert simple feature data frame to sp’s Spatial* class.
code chunk
childcare <- as_Spatial(childcare_sf)
mpsz <- as_Spatial(mpsz_sf)
sg <- as_Spatial(sg_sf)Notice that the geospatial data have been converted into their respective sp’s Spatial* classes now.
code chunk
childcareclass : SpatialPointsDataFrame
features : 1545
extent : 11203.01, 45404.24, 25667.6, 49300.88 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 2
names : Name, Description
min values : kml_1, <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>018989</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>1, MARINA BOULEVARD, #B1 - 01, ONE MARINA BOULEVARD, SINGAPORE 018989</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor=""> <th>NAME</th> <td>THE LITTLE SKOOL-HOUSE INTERNATIONAL PTE. LTD.</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>08F73931F4A691F4</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20200826094036</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center>
max values : kml_999, <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>829646</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>200, PONGGOL SEVENTEENTH AVENUE, SINGAPORE 829646</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td>Child Care Services</td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor=""> <th>NAME</th> <td>RAFFLES KIDZ @ PUNGGOL PTE LTD</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>379D017BF244B0FA</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20200826094036</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> code chunk
sgclass : SpatialPolygonsDataFrame
features : 60
extent : 2663.926, 56047.79, 16357.98, 50244.03 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 4
names : GDO_GID, MSLINK, MAPID, COSTAL_NAM
min values : 1, 1, 0, ISLAND LINK
max values : 60, 67, 0, SINGAPORE - MAIN ISLAND code chunk
mpszclass : SpatialPolygonsDataFrame
features : 323
extent : 2667.538, 56396.44, 15748.72, 50256.33 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 15
names : OBJECTID, SUBZONE_NO, SUBZONE_N, SUBZONE_C, CA_IND, PLN_AREA_N, PLN_AREA_C, REGION_N, REGION_C, INC_CRC, FMEL_UPD_D, X_ADDR, Y_ADDR, SHAPE_Leng, SHAPE_Area
min values : 1, 1, ADMIRALTY, AMSZ01, N, ANG MO KIO, AM, CENTRAL REGION, CR, 00F5E30B5C9B7AD8, 16409, 5092.8949, 19579.069, 871.554887798, 39437.9352703
max values : 323, 17, YUNNAN, YSSZ09, Y, YISHUN, YS, WEST REGION, WR, FFCCF172717C2EAF, 16409, 50424.7923, 49552.7904, 68083.9364708, 69748298.792 5.2 Converting Spatial* class into generic sp format
spatstat requires the analytical data in ppp object form. There is no direct way to convert a Spatial* classes into ppp object. We need to convert the Spatial* classes into Spatial object first.
code chunk
childcare_sp <- as(childcare, "SpatialPoints")
sg_sp <- as(sg, "SpatialPolygons")Let’s display the sp object properties
code chunk
childcare_spclass : SpatialPoints
features : 1545
extent : 11203.01, 45404.24, 25667.6, 49300.88 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs code chunk
sg_spclass : SpatialPolygons
features : 60
extent : 2663.926, 56047.79, 16357.98, 50244.03 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs There are key differences between the Spatial* classes and the generic sp objects. For example, let’s compare SpatialPointsDataFrame (a Spatial* class) and SpatialPoints (a generic sp object):
SpatialPointsclass: Represents a basic collection of spatial points within a specified coordinate system. This class is focused purely on the geometric data, meaning it only includes the locations (coordinates) of the points.SpatialPointsDataFrameclass: Builds on theSpatialPointsclass by integrating the spatial coordinates with a data frame containing attribute data. This allows for the storage of both spatial (geometric) data and non-spatial (attribute) data in one object, enabling each point to be associated with additional information.
5.3 Converting generic sp format into spatstat’s ppp format
Now let’s use as.ppp() function of spatstat to convert the spatial data into spatstat’s ppp object format.
code chunk
childcare_ppp <- as.ppp(childcare_sf)Warning in as.ppp.sf(childcare_sf): only first attribute column is used for
markscode chunk
childcare_pppMarked planar point pattern: 1545 points
marks are of storage type 'character'
window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] unitsLet us plot childcare_ppp and examine the difference.
code chunk
plot(childcare_ppp)Warning in default.charmap(ntypes, chars): Too many types to display every type
as a different characterWarning: Only 10 out of 1545 symbols are shown in the symbol map
We can take a quick look at the summary statistics of the newly created ppp object
code chunk
summary(childcare_ppp)Marked planar point pattern: 1545 points
Average intensity 1.91145e-06 points per square unit
Coordinates are given to 11 decimal places
marks are of type 'character'
Summary:
Length Class Mode
1545 character character
Window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] units
(34200 x 23630 units)
Window area = 808287000 square units
Note
Take note of the warning message regarding duplicates. In spatial point pattern analysis, the presence of duplicate points is a significant concern. The statistical methods used in analyzing spatial point patterns typically assume that the processes are simple, meaning that no two points should coincide.
5.4 Handling duplicated points
We can check the duplication in a ppp object by using the code chunk below.
code chunk
any(duplicated(childcare_ppp))[1] FALSEWe’ll use the multiplicity() function to count the number of coincident points
code chunk
multiplicity(childcare_ppp) [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[186] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[260] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[334] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[371] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[408] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[482] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[519] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[556] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[593] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[630] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[667] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[704] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[741] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[778] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[815] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1000] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1037] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1074] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1148] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1259] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1296] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1370] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1407] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1481] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1518] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1We can find out how many locations have more than one point, as shown in the code chunk below.
code chunk
sum(multiplicity(childcare_ppp) > 1)[1] 0There is no duplicate points here, but if we want to visualize the locations of duplicate points, we can plot the childcare data using the code chunk below.
code chunk
tmap_mode('view')tmap mode set to interactive viewingcode chunk
tm_shape(childcare) +
tm_dots(alpha=0.4,
size=0.05)code chunk
tmap_mode("plot")tmap mode set to plottingThere are three ways to address duplicate issue:
The simplest approach is to delete the duplicates. However, this will result in the loss of some potentially valuable point events.
Another solution is to use jittering, which introduces a small perturbation to the duplicate points so that they no longer occupy the exact same location.
The third approach involves making each point “unique” and then attaching the duplicates as marks, or attributes, to the original points. This method requires analytical techniques that account for these marks.
Jittering approach can be implemented as follows
code chunk
childcare_ppp_jit <- rjitter(childcare_ppp,
retry=TRUE,
nsim=1,
drop=TRUE)code chunk
any(duplicated(childcare_ppp_jit))[1] FALSE5.5 Creating owin object
When analyzing spatial point patterns, it is good practice to confine the analysis within a specific geographical area, such as the boundary of Singapore. In spatstat, an object called owin is specifically designed to represent such polygonal regions.
The following code demonstrates how to convert a SpatialPolygon object of Singapore into an owin object in spatstat.
code chunk
sg_owin <- as.owin(sg_sf)Let’s display the output using plot() and summary() function
code chunk
plot(sg_owin)
code chunk
summary(sg_owin)Window: polygonal boundary
50 separate polygons (1 hole)
vertices area relative.area
polygon 1 (hole) 30 -7081.18 -9.76e-06
polygon 2 55 82537.90 1.14e-04
polygon 3 90 415092.00 5.72e-04
polygon 4 49 16698.60 2.30e-05
polygon 5 38 24249.20 3.34e-05
polygon 6 976 23344700.00 3.22e-02
polygon 7 721 1927950.00 2.66e-03
polygon 8 1992 9992170.00 1.38e-02
polygon 9 330 1118960.00 1.54e-03
polygon 10 175 925904.00 1.28e-03
polygon 11 115 928394.00 1.28e-03
polygon 12 24 6352.39 8.76e-06
polygon 13 190 202489.00 2.79e-04
polygon 14 37 10170.50 1.40e-05
polygon 15 25 16622.70 2.29e-05
polygon 16 10 2145.07 2.96e-06
polygon 17 66 16184.10 2.23e-05
polygon 18 5195 636837000.00 8.78e-01
polygon 19 76 312332.00 4.31e-04
polygon 20 627 31891300.00 4.40e-02
polygon 21 20 32842.00 4.53e-05
polygon 22 42 55831.70 7.70e-05
polygon 23 67 1313540.00 1.81e-03
polygon 24 734 4690930.00 6.47e-03
polygon 25 16 3194.60 4.40e-06
polygon 26 15 4872.96 6.72e-06
polygon 27 15 4464.20 6.15e-06
polygon 28 14 5466.74 7.54e-06
polygon 29 37 5261.94 7.25e-06
polygon 30 111 662927.00 9.14e-04
polygon 31 69 56313.40 7.76e-05
polygon 32 143 145139.00 2.00e-04
polygon 33 397 2488210.00 3.43e-03
polygon 34 90 115991.00 1.60e-04
polygon 35 98 62682.90 8.64e-05
polygon 36 165 338736.00 4.67e-04
polygon 37 130 94046.50 1.30e-04
polygon 38 93 430642.00 5.94e-04
polygon 39 16 2010.46 2.77e-06
polygon 40 415 3253840.00 4.49e-03
polygon 41 30 10838.20 1.49e-05
polygon 42 53 34400.30 4.74e-05
polygon 43 26 8347.58 1.15e-05
polygon 44 74 58223.40 8.03e-05
polygon 45 327 2169210.00 2.99e-03
polygon 46 177 467446.00 6.44e-04
polygon 47 46 699702.00 9.65e-04
polygon 48 6 16841.00 2.32e-05
polygon 49 13 70087.30 9.66e-05
polygon 50 4 9459.63 1.30e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
(53380 x 33890 units)
Window area = 725376000 square units
Fraction of frame area: 0.4015.6 Combining point events object and owin object
In this last step of geospatial data wrangling, we will extract childcare events that are located within Singapore
code chunk
childcareSG_ppp = childcare_ppp[sg_owin]The output object combined both the point and polygon feature in one ppp object class
code chunk
summary(childcareSG_ppp)Marked planar point pattern: 1545 points
Average intensity 2.129929e-06 points per square unit
Coordinates are given to 11 decimal places
marks are of type 'character'
Summary:
Length Class Mode
1545 character character
Window: polygonal boundary
50 separate polygons (1 hole)
vertices area relative.area
polygon 1 (hole) 30 -7081.18 -9.76e-06
polygon 2 55 82537.90 1.14e-04
polygon 3 90 415092.00 5.72e-04
polygon 4 49 16698.60 2.30e-05
polygon 5 38 24249.20 3.34e-05
polygon 6 976 23344700.00 3.22e-02
polygon 7 721 1927950.00 2.66e-03
polygon 8 1992 9992170.00 1.38e-02
polygon 9 330 1118960.00 1.54e-03
polygon 10 175 925904.00 1.28e-03
polygon 11 115 928394.00 1.28e-03
polygon 12 24 6352.39 8.76e-06
polygon 13 190 202489.00 2.79e-04
polygon 14 37 10170.50 1.40e-05
polygon 15 25 16622.70 2.29e-05
polygon 16 10 2145.07 2.96e-06
polygon 17 66 16184.10 2.23e-05
polygon 18 5195 636837000.00 8.78e-01
polygon 19 76 312332.00 4.31e-04
polygon 20 627 31891300.00 4.40e-02
polygon 21 20 32842.00 4.53e-05
polygon 22 42 55831.70 7.70e-05
polygon 23 67 1313540.00 1.81e-03
polygon 24 734 4690930.00 6.47e-03
polygon 25 16 3194.60 4.40e-06
polygon 26 15 4872.96 6.72e-06
polygon 27 15 4464.20 6.15e-06
polygon 28 14 5466.74 7.54e-06
polygon 29 37 5261.94 7.25e-06
polygon 30 111 662927.00 9.14e-04
polygon 31 69 56313.40 7.76e-05
polygon 32 143 145139.00 2.00e-04
polygon 33 397 2488210.00 3.43e-03
polygon 34 90 115991.00 1.60e-04
polygon 35 98 62682.90 8.64e-05
polygon 36 165 338736.00 4.67e-04
polygon 37 130 94046.50 1.30e-04
polygon 38 93 430642.00 5.94e-04
polygon 39 16 2010.46 2.77e-06
polygon 40 415 3253840.00 4.49e-03
polygon 41 30 10838.20 1.49e-05
polygon 42 53 34400.30 4.74e-05
polygon 43 26 8347.58 1.15e-05
polygon 44 74 58223.40 8.03e-05
polygon 45 327 2169210.00 2.99e-03
polygon 46 177 467446.00 6.44e-04
polygon 47 46 699702.00 9.65e-04
polygon 48 6 16841.00 2.32e-05
polygon 49 13 70087.30 9.66e-05
polygon 50 4 9459.63 1.30e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
(53380 x 33890 units)
Window area = 725376000 square units
Fraction of frame area: 0.401Let’s plot the output object
code chunk
plot(childcareSG_ppp)Warning in default.charmap(ntypes, chars): Too many types to display every type
as a different characterWarning: Only 10 out of 1545 symbols are shown in the symbol map
6 First-order spatial point patterns analysis
In this section, we will learn how to perform first-order Spatial Point Pattern Analysis (SPPA) using the spatstat package. This sub-section will focus on:
- Deriving a Kernel Density Estimation (KDE) layer for visualizing and exploring the intensity of point processes.
- Conducting confirmatory spatial point pattern analysis using Nearest Neighbour statistics.
6.1 Kernel Density Estimation
6.1.1 Computing kernel density estimation using automatic bandwidth selection method
We will compute a kernel density using following configurations of density() of spatstat:
- bw.diggle() automatic bandwidth selection method. Other recommended methods are bw.CvL(), bw.scott() or bw.ppl().
- The smoothing kernel used is gaussian, which is the default. Other smoothing methods are: “epanechnikov”, “quartic” or “disc”.
- The intensity estimate is corrected for edge effect bias by using method described by Jones (1993) and Diggle (2010, equation 18.9). The default is FALSE.
code chunk
kde_childcareSG_bw <- density(childcareSG_ppp,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian") We’ll use plot() function to display the kernel density derived.
code chunk
plot(kde_childcareSG_bw)
The density values in the output range from 0 to 0.000035, which is difficult to interpret. This is because the default unit of measurement in SVY21 is meters, resulting in density values computed as the “number of points per square meter”.
It is helpful to know that you can retrieve the bandwidth used to compute the KDE layer using the following code.
code chunk
bw <- bw.diggle(childcareSG_ppp)
bw sigma
298.4095 6.1.2 Rescaling KDE values
We’ll use rescale.ppp() function to convert the unit of measurement from meter to kilometer.
code chunk
childcareSG_ppp.km <- rescale.ppp(childcareSG_ppp, 1000, "km")We can re-run density() using rescaled data set and plot the output kde map.
code chunk
kde_childcareSG.bw <- density(childcareSG_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_childcareSG.bw)
Notice that the output image appears identical to the earlier version; the only difference is in the data values (as shown in the legend).
6.2 Working with different automatic bandwidth methods
In addition to bw.diggle(), there are three other spatstat functions that can be used to determine the bandwidth: bw.CvL(), bw.scott(), and bw.ppl().
Let’s examine the bandwidth values returned by these automatic bandwidth selection methods using the following code.
code chunk
bw.CvL(childcareSG_ppp.km) sigma
4.543278 code chunk
bw.scott(childcareSG_ppp.km) sigma.x sigma.y
2.224898 1.450966 code chunk
bw.ppl(childcareSG_ppp.km) sigma
0.3897114 code chunk
bw.diggle(childcareSG_ppp.km) sigma
0.2984095 Baddeley et al. (2016) recommend using the bw.ppl() algorithm, as it tends to produce more appropriate bandwidth values when the pattern primarily consists of tight clusters. However, they also note that if the goal of a study is to detect a single tight cluster amidst random noise, the bw.diggle() method often performs best.
The following code will be used to compare the outputs of the bw.diggle and bw.ppl methods.
code chunk
kde_childcareSG.ppl <- density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="gaussian")
par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "bw.diggle")
plot(kde_childcareSG.ppl, main = "bw.ppl")
6.3 Working with different kernel methods
By default, the kernel method used in density.ppp() is Gaussian. However, there are three other options available: Epanechnikov, Quartic, and Disc.
The following code will be used to compute three additional kernel density estimations using these alternative kernel functions.
code chunk
par(mfrow=c(2,2))
plot(density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="gaussian"),
main="Gaussian")
plot(density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="epanechnikov"),
main="Epanechnikov")Warning in density.ppp(childcareSG_ppp.km, sigma = bw.ppl, edge = TRUE, :
Bandwidth selection will be based on Gaussian kernelcode chunk
plot(density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="quartic"),
main="Quartic")Warning in density.ppp(childcareSG_ppp.km, sigma = bw.ppl, edge = TRUE, :
Bandwidth selection will be based on Gaussian kernelcode chunk
plot(density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="disc"),
main="Disc")Warning in density.ppp(childcareSG_ppp.km, sigma = bw.ppl, edge = TRUE, :
Bandwidth selection will be based on Gaussian kernel
7 Fixed and adaptive KDE
7.1 Computing KDE by using fixed bandwidth
Next, we will compute a KDE layer by defining a bandwidth of 600 meters. > Notice that in the code below, the sigma value is set to 0.6. This is because the unit of measurement for the childcareSG_ppp.km object is in kilometers, so 600 meters is equivalent to 0.6 kilometers.
code chunk
kde_childcareSG_600 <- density(childcareSG_ppp.km, sigma=0.6, edge=TRUE, kernel="gaussian")
plot(kde_childcareSG_600)
7.2 Computing KDE by using adaptive bandwidth
The fixed bandwidth method is highly sensitive to skewed distributions of spatial point patterns across geographical units, such as urban versus rural areas. One way to address this issue is by using adaptive bandwidth instead.
In this section, we will learn how to derive adaptive kernel density estimation using the density.adaptive() function from the spatstat package.
code chunk
kde_childcareSG_adaptive <- adaptive.density(childcareSG_ppp.km, method="kernel")
plot(kde_childcareSG_adaptive)
We can compare the outputs of fixed and adaptive kernel density estimations using the following code.
code chunk
par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "Fixed bandwidth")
plot(kde_childcareSG_adaptive, main = "Adaptive bandwidth")
7.3 Converting KDE output into grid object
The result remains the same; we’ve simply converted it to make it suitable for mapping purposes.
code chunk
gridded_kde_childcareSG_bw <- as(kde_childcareSG.bw, "SpatialGridDataFrame")
spplot(gridded_kde_childcareSG_bw)
7.3.1 Converting gridded output into raster
We will convert the gridded kernel density objects into a RasterLayer object using the raster() function from the raster package.
code chunk
kde_childcareSG_bw_raster <- raster(kde_childcareSG.bw)Let’s examine the properties of the kde_childcareSG_bw_raster RasterLayer.
code chunk
kde_childcareSG_bw_rasterclass : RasterLayer
dimensions : 128, 128, 16384 (nrow, ncol, ncell)
resolution : 0.4170614, 0.2647348 (x, y)
extent : 2.663926, 56.04779, 16.35798, 50.24403 (xmin, xmax, ymin, ymax)
crs : NA
source : memory
names : layer
values : -1.005814e-14, 28.51831 (min, max)Notice that the crs property is NA.
7.3.2 Assigning projection systems
The following code will be used to add CRS information to the kde_childcareSG_bw_raster RasterLayer.
code chunk
projection(kde_childcareSG_bw_raster) <- CRS("+init=EPSG:3414")
kde_childcareSG_bw_rasterclass : RasterLayer
dimensions : 128, 128, 16384 (nrow, ncol, ncell)
resolution : 0.4170614, 0.2647348 (x, y)
extent : 2.663926, 56.04779, 16.35798, 50.24403 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +units=m +no_defs
source : memory
names : layer
values : -1.005814e-14, 28.51831 (min, max)Notice that the crs property is completed now.
7.4 Visualising the output in tmap
Finally, we will display the raster on a cartographic-quality map using the tmap package.
code chunk
tm_shape(kde_childcareSG_bw_raster) +
tm_raster("layer", palette = "viridis") +
tm_layout(legend.position = c("right", "bottom"), frame = FALSE)
Notice that the raster values are explicitly encoded onto the raster pixels using the values in the “v” field.
7.5 Comparing Spatial Point Patterns using KDE
In this section, we will learn how to compare the KDE of childcare facilities in the planning areas of Punggol, Tampines, Chua Chu Kang, and Jurong West.
7.5.1 Extracting study area
Let us extract the target planning areas.
code chunk
pg <- mpsz_sf %>%
filter(PLN_AREA_N == "PUNGGOL")
tm <- mpsz_sf %>%
filter(PLN_AREA_N == "TAMPINES")
ck <- mpsz_sf %>%
filter(PLN_AREA_N == "CHOA CHU KANG")
jw <- mpsz_sf %>%
filter(PLN_AREA_N == "JURONG WEST")Plot target planning areas
code chunk
par(mfrow=c(2,2))
plot(pg, main = "Punggol")Warning: plotting the first 9 out of 15 attributes; use max.plot = 15 to plot
all
code chunk
plot(tm, main = "Tampines")Warning: plotting the first 9 out of 15 attributes; use max.plot = 15 to plot
all
code chunk
plot(ck, main = "Choa Chu Kang")Warning: plotting the first 10 out of 15 attributes; use max.plot = 15 to plot
all
code chunk
plot(jw, main = "Jurong West")Warning: plotting the first 9 out of 15 attributes; use max.plot = 15 to plot
all
7.5.2 Creating owin object
We will convert these sf objects into owin objects that is required by spatstat.
code chunk
pg_owin = as.owin(pg)
tm_owin = as.owin(tm)
ck_owin = as.owin(ck)
jw_owin = as.owin(jw)7.5.3 Combining childcare points and the study area
Using the code below, we can extract childcare facilities within specific regions for further analysis.
code chunk
childcare_pg_ppp = childcare_ppp_jit[pg_owin]
childcare_tm_ppp = childcare_ppp_jit[tm_owin]
childcare_ck_ppp = childcare_ppp_jit[ck_owin]
childcare_jw_ppp = childcare_ppp_jit[jw_owin]Next, the rescale.ppp() function is used to transform the unit of measurement from meters to kilometers.
code chunk
childcare_pg_ppp.km = rescale.ppp(childcare_pg_ppp, 1000, "km")
childcare_tm_ppp.km = rescale.ppp(childcare_tm_ppp, 1000, "km")
childcare_ck_ppp.km = rescale.ppp(childcare_ck_ppp, 1000, "km")
childcare_jw_ppp.km = rescale.ppp(childcare_jw_ppp, 1000, "km")The following code is used to plot the four study areas along with the locations of the childcare centers.
code chunk
par(mfrow=c(2,2))
plot(childcare_pg_ppp.km, main="Punggol")Warning in default.charmap(ntypes, chars): Too many types to display every type
as a different characterWarning: Only 10 out of 61 symbols are shown in the symbol mapcode chunk
plot(childcare_tm_ppp.km, main="Tampines")Warning in default.charmap(ntypes, chars): Too many types to display every type
as a different characterWarning: Only 10 out of 89 symbols are shown in the symbol mapcode chunk
plot(childcare_ck_ppp.km, main="Choa Chu Kang")Warning in default.charmap(ntypes, chars): Too many types to display every type
as a different characterWarning: Only 10 out of 61 symbols are shown in the symbol mapcode chunk
plot(childcare_jw_ppp.km, main="Jurong West")Warning in default.charmap(ntypes, chars): Too many types to display every type
as a different characterWarning: Only 10 out of 88 symbols are shown in the symbol map
7.5.4 Computing KDE
The following code will compute the KDE for these four planning areas. The bw.diggle method is used to determine the bandwidth for each area.
code chunk
par(mfrow=c(2,2))
plot(density(childcare_pg_ppp.km,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian"),
main="Punggol")Warning: Berman-Diggle Cross-Validation criterion was minimised at right-hand
end of interval [0, 0.245]; use argument 'hmax' to specify a wider interval for
bandwidth 'sigma'code chunk
plot(density(childcare_tm_ppp.km,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian"),
main="Tampines")
plot(density(childcare_ck_ppp.km,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian"),
main="Choa Chu Kang")
plot(density(childcare_jw_ppp.km,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian"),
main="Jurong West")
7.5.5 Computing fixed bandwidth KDE
For comparison purposes, we will use 250m as the bandwidth.
code chunk
par(mfrow=c(2,2))
plot(density(childcare_pg_ppp.km,
sigma=0.25,
edge=TRUE,
kernel="gaussian"),
main="Punggol")
plot(density(childcare_tm_ppp.km,
sigma=0.25,
edge=TRUE,
kernel="gaussian"),
main="Tampines")
plot(density(childcare_ck_ppp.km,
sigma=0.25,
edge=TRUE,
kernel="gaussian"),
main="Choa Chu Kang")
plot(density(childcare_jw_ppp.km,
sigma=0.25,
edge=TRUE,
kernel="gaussian"),
main="Jurong West")
8 Nearest neighbour analysis
In this section, we will perform the Clark-Evans test of aggregation for a spatial point pattern using the clarkevans.test() function from the spatstat package.
The test hypotheses are:
- H₀: The distribution of childcare services is random.
- H₁: The distribution of childcare services is not random.
We will use a 95% confidence interval.
8.1 Testing spatial point patterns using Clark and Evans Test
code chunk
clarkevans.test(childcareSG_ppp,
correction="none",
clipregion="sg_owin",
alternative=c("clustered"),
nsim=99)
Clark-Evans test
No edge correction
Z-test
data: childcareSG_ppp
R = 0.55631, p-value < 2.2e-16
alternative hypothesis: clustered (R < 1)Given that the p-value is less than 0.05, we can reject the null hypothesis and conclude that the distribution of childcare centers in Singapore is not random but rather clustered.
Using the clarkevans.test() function from spatstat, we conducted a Clark-Evans test to assess the aggregation of childcare centers in Choa Chu Kang planning area.
code chunk
clarkevans.test(childcare_ck_ppp,
correction="none",
clipregion=NULL,
alternative=c("two.sided"),
nsim=999)
Clark-Evans test
No edge correction
Z-test
data: childcare_ck_ppp
R = 0.9208, p-value = 0.2367
alternative hypothesis: two-sidedThe locations of childcare in Choa Chu Kang appear to be randomly distributed, with no strong evidence of them being concentrated in specific areas or evenly spaced apart.
Using the clarkevans.test() function from spatstat, we conducted a Clark-Evans test to assess the aggregation of childcare centers in Tampines planning area.
code chunk
clarkevans.test(childcare_tm_ppp,
correction="none",
clipregion=NULL,
alternative=c("two.sided"),
nsim=999)
Clark-Evans test
No edge correction
Z-test
data: childcare_tm_ppp
R = 0.78493, p-value = 0.0001038
alternative hypothesis: two-sidedThe locations of childcare centers in Tampines are significantly clustered, with strong evidence suggesting that they tend to be closer together rather than being randomly distributed or evenly spaced apart.
9 Reference
Kam, T. S. 1st Order Spatial Point Patterns Analysis Methods. R for Geospatial Data Science and Analytics. https://r4gdsa.netlify.app/chap04